basic uploading consists of a simple HTML form for files. The forms sends this information to a PHP page that can copy the file to the desired place.
Adding ability to explore directories isn't difficult as it is a pretty basic while loop examining a directories contents.
It's all in the manuel
There are also articles on this very site that describe how to handle uploads.
If you want the HTML for the form, you could look at the source for the "reply" page in this forum because there is a file upload form in it.
EDIT: By the way, allowing users to upload stuff to your site is extremely dangerous. Stuff like that may even get you kicked off your server.